MAT 322-01 - Advanced Topics in Algebra: Elliptic Curves

4 credits (Spring) Elliptic curves play a crucial role in modern mathematics from pure mathematics (the proof of Fermat’s Last Theorem) to applied mathematics (elliptic-curve cryptography). These surprisingly sophisticated objects are solutions to cubic equations. To be able to understand how these curves are used, we need to develop their algebraic properties, particularly a beautiful group structure we can create on the solutions. There will be a research component to the class.